As anger is something that Judaism firmly discourages, it's interesting to think that we might be missing out on the potential to think more rationally.

In reality, I believe the study needs to be more thorough and take into account that passion, and elevated excitement is what improves the rationality of people's decisions, not anger exactly.

We can see this clearly in a lively chevruta. Personally, it always bothers me when I start to get riled up and argue with someone even over gemara, because I'm worried about being less rational. Interesting to note that this striving and argumentation in study, especially when it gets heated and excited actually brings out clearer points, and more thorough logic.

Perhaps this was part of what Rebbe Nachman meant in his Torah [also discussed here] about people creating a vacuum between them during their study into which new worlds could be created. The pressure and intensity of the back and forth allows for the purest truest logic to emerge.

Ironically, I have a tendency to bat down false logic in a harsh manner that sometimes makes people feel I'm upset. I always try to explain that the intensity of my rejection was focused at their logic, not at them personally, now at least I understand why I do that. I still need to change it so that I don't offend or hurt others and internalize it more.

This is true of anger in general, we are instructed by Chazal that even in situations that call for anger, in raising children for example, we must be completely calm on the inside and only put on an act of anger. Otherwise, when we really get angry, there is an element of not recognizing HaShem in his creation, which is a denial of HaShem, which is at its root Avodah Zarah. If chas v'shalom we do get angry, Chazal teach that we could (chas v'shalom) lose everything we've accomplished.